Optical transmission system

ABSTRACT

In an optical transmission system, SPM influences on the degradation of wave forms are canceled by setting an amount of compensation of a dispersion compensator at about 50% of the total amount of dispersion of an optical fiber transmission line so that a received wave form is substantially not varied, even if light intensity is varied. When a plurality of dispersion compensator are used, the number of compensators is optimized by setting the arrangement interval in the vicinity of the receiving end to a small value. Further, in a transmission line, in which amounts of dispersion of optical fibers have positive and negative fluctuations, the smallest transmission distance of a transmission system is increased by effecting dispersion compensation so that an expected value of the total amount of dispersion of the transmission line is abnormal dispersion.

BACKGROUND OF THE INVENTION

The present invention relates to an optical transmission system using anIM (Intensity Modulation) method, which is one type of optical fibercommunication methods.

Recently in the field of optical fiber communication, increase in signaltransmission speed and increase in transmission distance have beenrapidly developed. One of the most important factors restricting thetransmission distance in such a superhigh speed/long distancetransmission is "dispersion" due to optical fiber. Dispersion is aphenomenon, by which lights having different wavelengths are transmittedwith different speeds in the optical fiber. Optical spectre of lightsignals modulated with a high speed contains components having differentwavelengths and these components having different wavelengths reach areceiving end at different points of time under influences of thedispersion. It is known that, as the result, large waveform distortiontakes place in light waveform after the transmission. A method calleddispersion compensation is conceived as a method for avoiding suchinfluences of dispersion. This is a method for preventing waveformdistortion after the transmission, by which mediums (optical fiber orgrating) having dispersion characteristics opposite to those of thetransmission line are inserted into the course thereof so that the meandispersion of the transmission line is approximately zero.

On the other hand, nonlinear effects of the optical fiber are known asanother factor restricting the transmission distance for optical fibercommunication. In particular, in the optical transmission by theintensity modulation method, self phase modulation (hereinbelowabbreviated to SPM) effect, which is one of the nonlinear effects of theoptical fiber, gives rise to a serious problem. SPM is a phenomenon, bywhich a refractive index of the optical fiber varies pro-portionally tovariations in the intensity of optical signals, and as the result, extraphase modulation, i.e. frequency chirp (variations in light frequency),is superposed on the light signals in the optical fiber. Light signalshaving such frequency chirp give rise to important waveform variationsafter the transmission because of influences of the dispersion, whichthe optical fiber has. Such influences of SPM is reported in 1"Nonlinear Fiber Optics", Academic Press, 1992, (ISBN 0-12-045140-9), 2Technical Reports of Institute of Electronics, Information andCommunication Engineers (Japan) OCS92-52, by Kikuchi, et al., ElectronicCommunication Information Society (1992), etc.

Heretofore several examples, in which the dispersion compensation iseffected, have been reported, also in case where influences of SPM aregreat. However, the dispersion compensation has been effected thereinmerely so that the dispersion of the whole transmission line is zerojust as in the prior art techniques. Further influences, which the SPMhas on the dispersion compensated transmission, are almost not studied.

SUMMARY OF THE INVENTION

The object of the present invention is to provide an opticaltransmission system using dispersion compensation method, takinginfluences of SPM into account.

Denoting the light intensity in the optical fiber at a point Z displacedfrom an optical transmitter by a distance z by P(z) and the amount ofdispersion from the point Z to an optical receiver (including dispersionof the optical dispersion compensator) by D(z), the above object can beachieved by setting the position of the optical dispersion compensatorand the amount of dispersion so that a value obtained by integrating aproduct P(z)·D(z) from z=0 to L is approximately zero.

Particularly, in the case where a plurality of optical dispersioncompensators are used, denoting a point directly after the i-th opticaldispersion compensator counted from the optical transmitter by Z_(i) andthe amount of dispersion from the point Z to the point Z_(i) (includingdispersion of the optical dispersion compensator) by D_(i) (z), theobject can be achieved by setting the positions of the opticaldispersion compensators and the amounts of dispersion so that valuesobtained by integrating products P(z)·D_(i) (z) from z=0 to Z_(i) areapproximately zero for all i.

Further, in case where an optical dispersion compensator is disposedbefore the optical transmitter, it can be achieved by setting the amountof dispersion C of the dispersion compensator so as to be approximately{1/(aL)-(N+1)/(2N)} times as great as the amount of dispersion B of thetransmission line (where a is the loss factor of the optical fiber, L isthe total transmission distance, and N is the number of fiber sections).

It can be achieved also by disposing dispersion compensators in theneighborhood of the receiving end so that arrangement intervaltherebetween is smaller than that between dispersion compensators in theneighborhood of the transmitting end. It can be achieved moreefficiently particularly by disposing dispersion compensators at suchpositions that distortion in waveform directly before differentdispersion compensators are in accordance with each other. Further, incase where the amount of dispersion in different fiber sections and theoptical output intensity of different optical amplifier are almostconstant and the influences of SPM are great, it can be achieved bysetting the interval 1_(i) between i-th and (i+1)-th dispersioncompensators so as to be approximately {√-√(i-1)} times as great as 1₁,being the interval between the optical transmitter and the firstdispersion compensator.

Furthermore it can be achieved by disposing dispersion compensators attwo positions, i.e. directly after the optical transmitter and directlybefore the optical receiver, and by transmitting signals after havingenlarged satisfactorily the width of the light waveform by means of thefirst dispersion compensator with respect to the width of the lightwaveform to be transmitted.

In the case where dispersions of optical fibers constituting differentfiber sections have statistical fluctuations to a certain extent, theobject can be achieved by effecting dispersion compensation so that anexpected value of the total dispersion including dispersion produced bydispersion compensators in the course of the transmission line ispositive dispersion (anomalous dispersion). Specifically when denotingthe transmittable distance by L, in the case where all the amounts ofdispersion of optical fiber sections are minimum and dispersioncompensation is zero, and a positive dispersion compensation, by whichtransmission over the distance L is made possible, by C, in the casewhere all the amounts of dispersion of optical fiber sections aremaximum, the object can be achieved by setting the amounts of dispersioncompensation of the dispersion compensators in a region between 0 and C.It can be achieved more efficiently particularly by setting the amountsof dispersion compensation so that distortion in waveform after thetransmission are approximately in accordance with each other in twocases where dispersions in all the optical fibers are minimum and wheredispersions in all the optical fibers are maximum.

Further, even in the case where transmission is effected by using a zerodispersion wavelength in the transmission line, the object can beachieved by effecting dispersion compensation. It is achieved bycompensating deviation of dispersion of the transmission line asfollows. Denoting the light intensity in the optical fiber at a point Zfar from an optical transmitter by a distance z by P(z) and the amountof dispersion from the point Z to an optical receiver (includingdispersion of the optical dispersion compensator) by D(z), the aboveobject can be achieved by setting the position of the optical dispersioncompensator and the amount of dispersion so that a value obtained byintegrating a product P(z)·D(z) from z=0 to L is approximately zero. Inthe case where dispersions have statistical fluctuations to a certainextent, the object can be achieved also by effecting positive dispersioncompensation. Furthermore, in the case where a transmission section,which is the first half of the transmission line, has the smallestdispersion, while the other transmission section, which is the secondhalf of the transmission line, has the greatest dispersion, the objectcan be achieved more efficiently by setting the amounts of dispersion sothat worsenings in waveform of the received wave in the two sections areapproximately in accordance with each other.

Frequency chirp produced by SPM is generated, distributed over the wholelength of the transmission line and subjected to dispersion after thegeneration point, which gives rise to a worsening of the waveform.Averaged over the whole length of the transmission line, the center ofgeneration points of SPM is almost in the neighborhood of the center ofthe transmission line, in the case where the number of fiber sections Nis sufficiently great. Consequently by effecting dispersion compensationfor an approximately half of the amount of dispersion of thetransmission line it is possible to reduce dispersion, to which the SPMis subjected, equivalently to zero. In this way, for example, even ifthe intensity of light output of a optical amplifier is varied, it ispossible that received waveform is not varied.

Further, since the frequency chirp produced by SPM is accumulated duringtransmission, variations in optical waveform are produced more easily byinfluences of dispersion in the second half of the transmission line.Therefore, in the case where a plurality of dispersion compensator areprovided, it is possible to increase the dispersion compensation effectby decreasing the arrangement interval with decreasing distance from thereceiving end. In addition, in the case where dispersion compensation iseffected, taking influences of SPM into account, if the waveform ischanged remarkably during transmission, it is impossible to restore theoriginal waveform even after the dispersion compensation. However it isdisadvantageous in cost to increase excessively the number of dispersioncompensators. Therefore, it is possible to optimize the number ofdispersion compensators by inserting a dispersion compensator every timewhen worsening of the waveform after the transmission reaches apredetermined value.

Since worsening of the waveform by SPM is proportional to the magnitudeof intensity modulated components, which transmitted waveforms have, itis possible to suppress influences of the SPM by inserting a dispersioncompensator directly after the optical transmitter and effectingtransmission after having increased sufficiently the width of lightwaveforms with respect to the width of light waveforms to betransmitted.

In the case where dispersions of optical fibers constituting differentfiber sections have statistical fluctuations in a certain extent, thesmallest transmission distance of the transmission system is restrictedusually when all dispersions of the transmission line are fluctuated onthe negative dispersion side. Consequently, it is possible to increasethe smallest transmission distance of the transmission system byeffecting dispersion compensation so that an expected value of the totaldispersion is positive dispersion (anomalous dispersion). In particular,the smallest transmission distance of the transmission system can beincreased at most by setting the amounts of dispersion compensation sothat worsenings of the waveform after the transmission are approximatelyin accordance with each other in two cases where dispersions in all theoptical fibers are minimum and where dispersions in all the opticalfibers are maximum.

Also in the case where transmission is effected by using a zerodispersion wavelength in the transmission line, it is possible to reduceworsening of the waveform by SPM and to increase the transmissiondistance by compensating deviations in the dispersion of thetransmission line by using dispersion compensation. Further, even in thecase where there are statistical fluctuations to a certain extent in thedispersion, it is possible to increase the smallest transmissiondistance of the transmission system by effecting dispersion compensationon the positive dispersion side.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a diagram showing a construction representing a firstembodiment of the present invention;

FIG. 2 is a diagram indicating light intensity distribution in anoptical fiber transmission line;

FIG. 3 is a diagram showing a construction representing a secondembodiment of the present invention;

FIG. 4 shows a relationship between light output of an optical amplifierand an eye opening penalty of received waveform;

FIGS. 5A and 5B show eye patterns of received waveforms;

FIG. 6 indicates a relationship between the amount of dispersioncompensation and the phase margin of received waveforms;

FIG. 7 is a diagram showing a construction representing a thirdembodiment of the present invention;

FIG. 8 is a diagram showing a construction representing a fourthembodiment of the present invention;

FIG. 9 is a diagram showing a construction representing a fifthembodiment of the present invention;

FIG. 10 is a diagram showing a construction representing a sixthembodiment of the present invention;

FIG. 11 is a diagram showing a construction representing a seventhembodiment of the present invention;

FIG. 12 is a diagram showing a construction representing a eighthembodiment of the present invention;

FIG. 13 is a diagram showing a construction representing a ninthembodiment of the present invention;

FIG. 14 is a diagram showing a construction representing a tenthembodiment of the present invention;

FIG. 15 indicates a relationship between the amount of dispersioncompensation and the transmission distance; and

FIGS. 16A and 16B show the worst dispersion arrangements in the zerodispersion wavelength transmission.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

FIG. 1 is a diagram showing a construction representing a firstembodiment of the present invention. Intensity modulated lighttransmitted by an optical transmitter 100 is transmitted through atransmission line, in which optical fibers 101 and optical amplifiers102, are arranged alternately. One or a plurality of dispersioncompensators 103 are disposed in the course of the transmission line andtransmitted light signals are received by an optical receiver 104. Thefigure shows an example, in which two dispersion compensators 103 aredisposed.

In a prior art dispersion compensated transmission the amount ofdispersion compensation C of each dispersion compensator is set so as tocompensate the dispersion of the optical fiber directly preceding therelevant dispersion compensator so that the total amount of dispersionof the transmission line including the dispersion compensators is zero.In such a prior art dispersion compensated transmission influences ofthe worsening or degradation of the waveform by SPM are not taken intoaccount.

On the contrary, according to the present invention, denoting the lightintensity in the optical fiber at a point Z for displaced from atransmitting end by a distance z by P(z) and the amount of dispersion ofthe transmission line (including dispersion of the dispersioncompensator) from the point Z to the optical receiver 104 by D(z), thevalue of C and the position of the dispersion compensator are so setthat the integral of a product P(z)·D(z) from z=0 to L is approximatelyzero. In this way, transmission, in which influences of the SPM, whichis a nonlinear effect produced in the optical fiber, are approximatelycancelled, is made possible. The reason therefor can be explained asfollows.

FIG. 2 shows light intensity distribution P(z) in the optical fibertransmission line. Since the magnitude of frequency chirps produced bySPM in the course of the optical fiber is proportional to the lightintensity in the optical fiber, it is distributed as indicated in FIG.2. It is conceivable that these frequency chirps give rise to worseningof the waveform after the transmission under influences of the amount ofdispersion D(z) between the generation point z and the optical receiver104. By the method indicated in the reference--described previously itis conceivable that worsening of the waveform is proportional to a valueobtained by integrating the product P(z)·D(z) from the transmitting endto the receiving end. Consequently it is possible to reduce theworsening of the waveform by SPM almost to 0 by effecting dispersioncompensation so that this values is almost 0. This condition can beexpressed as indicated by Eq. (1). ##EQU1##

A value obtained by dividing the left side of this equation by the meanlight intensity represents the amount of dispersion from the averagedcenter (center of gravity) of the frequency chirps produced by SPM tothe receiving end. Eq. (1) means that compensation is effected so thatthis value is zero, i.e. the averaged amount of dispersion, to which thefrequency chirps by SPM is subjected, is zero. It is possible tocompensate approximately completely influences of SPM by effectingdispersion compensation in this way.

FIG. 3 shows a second embodiment of the present invention, which is anexample in which only one dispersion compensator 103 is used, which isdisposed before the optical receiver 104. In the present embodiment,denoting the total amount of dispersion of the transmission line by B,the value of the amount of dispersion compensation C is givenapproximately by Eq. (2), ##EQU2## where a is the loss factor of theoptical fiber, L is the total transmission distance, and N is the numberof fiber sections. The above equation is an approximate solutionobtained by solving Eq. (1), assuring that light output intensities ofthe optical transmitter 100 and the optical amplifier 102 areapproximately equal to each other. For example, letting a=0.25 dB/km,L=1000 km, and N=10, the amount of dispersion compensation in thepresent embodiment is about 53% (the sign being reversed) of the totalamount of dispersion of the transmission line. FIG. 4 shows an aspect ofvariations in an eye opening penalty of the received waveform withrespect to the light output intensity of the optical amplifier, usingthe amount of dispersion compensation as a parameter. In thiscalculation it is assured that bit rate is 5 Gbps, total transmissiondistance L=1000 km, N=10, amount of dispersion of optical fiber D=-3.5ps/nm/km. The three curves in FIG. 1 indicate effects withoutcompensation, with 53% compensation (by the present method), and with100% compensation (by the prior art method), respectively. It isconfirmed that in the two examples, in which dispersion compensation iseffected, eye opening worsening after the transmission is suppressed toa small value, even in a region where light output intensity is high(influences of SPM being great), with respect to the case where nodispersion compensation is effected. From this figure it seems that eyeopening worsening is smaller in the example, in which 100% compensationis effected, than in the case where 53% compensation is effected.However, this is because in the case of the 100% compensation influencesof SPM are not cancelled and compression of the transmitted waveformtakes place by the effects of SPM. This aspect can be confirmed from theeye patterns of the received waveform indicated in FIGS. 5A and 5B. FIG.5A shows the example of 100% compensation, where (a) and (b) indicateeye patterns of the received waveform for light output intensities of -3dBm and +3 dBm, respectively. It can be verified that great waveformcompression takes place and the received waveform is varied remarkably,when light output increases. On the contrary, in the example of 53%compensation by the present method indicated in FIG. 5B, it can beconfirmed that the received waveform is almost not changed, even in thecase where light intensity is varied, because influences of SPM areapproximately cancelled. As described above, since the received waveformdoesn't vary by the present method even if the light output intensity isvaried, advantages are obtained that setting of a discrimination levelof the optical receiver is easy and that phase margin of the receivedwaveform increases. FIG. 6 shows a relationship between the amount ofdispersion and the phase margin of the transmitted waveform. It can beverified that the phase margin is the greatest in the neighborhood ofthe 53% dispersion compensation by the present method. Further it can beverified that the present invention is efficient in a region of thedispersion compensation from 20% to 80%.

Further, particularly in case where the dispersion, the section length,etc. of the different fiber sections are not constant, necessary amountsof dispersion compensation can be calculated, using Eq. (3). ##EQU3##where P_(i) is the light intensity inputted to an i-th fiber sectioncounted from the transmitting side, and D_(i) and L_(i) are the amountof dispersion and the length of the fiber in the i-th section.

FIG. 7 shows a third embodiment of the present invention, which is anexample, in which a plurality of dispersion compensators 104 arearranged, distributed in a transmission line. In this case the highestefficiency can be obtained by setting the dispersion compensators sothat the condition described previously to cancel SPM is satisfieddirectly after each of them. That is, denoting the number of dispersioncompensators by M; the position of an i-th dispersion compensatorcounted from the optical transmitter 100 (distance from the transmittingend) by z₁ ; the amount of compensation by C_(i) ; the light intensityin the optical fiber at a point Z far from the transmitting end by adistance z by P(z); and the amount of dispersion between the points Zand z_(i) by D_(i) (z), the value of C_(i) and the position of therelevant dispersion compensator are so set that a value obtained byintegrating a product P(z)·D_(i) (z) from z=0 to z_(i) is approximatelyzero for all i. In this way transmission is possible by which influencesof SPM, which are nonlinear effects produced in the optical fiber, areapproximately cancelled.

For the dispersion compensators used for realizing the present inventionany optical element having dispersing characteristics can be used. Asexamples of such an optical element there are an optical element usingreflection by grating pair or grating, an optical element using aFabry-Perot interferometer, a Mach-Zehnder interferometer, etc., anelement using dispersing characteristics of an absorption edge of anoptical semiconductor device, etc. Further it is also possible to use anoptical fiber having dispersing characteristics opposite to those of thetransmission line as a dispersion compensating element. Particularly incase where a transmission wavelength of 1.55 μm is used, it is efficientto use an optical fiber having a zero dispersion wavelength at 1.3 μm,etc. as a dispersion compensating fiber. A fourth embodiment (FIG. 8)and a fifth embodiment (FIG. 9) of the present invention are examples,in which dispersion compensating fiber 105 itself is used as aconstituent element of a part or the whole of the transmission line orthe fiber sections. The present method is efficient also in the casewhere influences of SPM within the dispersion compensating fiber cannotbe neglected and the amount of dispersion compensation can be calculatedby the method identical to that described above.

FIG. 10 shows a sixth embodiment of the present invention, whichindicates the optimum arrangement of dispersion compensators. The figureshows an example, in which there are disposed three dispersioncompensators. In this figure optical amplifiers are omitted. By theprior art method it was thought that the interval between consecutivedispersion compensators is constant. However, in the present embodiment,denoting the interval between the optical transmitter and the firstdispersion compensator by 1₁, the interval between the first dispersioncompensator and the second dispersion compensator by 1₂, and theinterval between the second dispersion compensator and the thirddispersion compensator by 1₃, the dispersion compensators 106, 107 and108 are arranged so that 1₁ ≧1₂ ≧1₃. The reason therefor is as follows.For example, even if a case where dispersion compensation is effected sothat worsening of the waveform after the transmission is reduced to zeroby means of each of the dispersion compensators is taken into account,although worsening of the waveform can be compensated, frequency chirpby SPM cannot be cancelled, but it is accumulated during transmission.Therefore it is possible to decrease the number of necessary dispersioncompensators by decreasing the interval between consecutive dispersioncompensators with decreasing distance from the receiving end. In thiscase the amount of compensation may be set so as to compensate 100% ofthe amount of dispersion of the directly preceding transmission fibersection and also to cancel influences of SPM as indicated in theembodiment described above of the present invention.

In the case where the number of dispersion compensators is optimized, itis most suitable to arrange dispersion compensators so that worseningsin waveform directly before different dispersion compensators are inaccordance with each other. That is, a first dispersion compensator isarranged at a position where worsening of the waveform in the opticalfiber transmission line reaches a predetermined value to remedy theworsening of the waveform and thereafter the succeeding dispersioncompensator is inserted at a point where it reaches again thepredetermined value. By repeating this process it is possible to obtainthe greatest transmission distance with a given number of dispersioncompensators. As a method for evaluating the amount of worsening of thewaveform, e.g. a point where the width of the received waveform isincreased by 10% or a point where the amount of eye opening worsening is1 dB may be adopted. In particular, in case where the worsening inwaveform by SPM limits the transmission distance, the arrangement ofdispersion compensators can be optimized by setting the interval 1_(i)of the i-th dispersion compensator so as to be {√i-√(i-1)} times asgreat as 1₁.

FIG. 11 shows a seventh embodiment of the present invention, which is anexample, in which dispersion compensators are arranged in a firstportion with an almost equal interval and dispersion compensators arearranged after a point on the way with smaller intervals. In the firstportion of the fiber transmission line, since worsening of the waveformis produced more strongly by dispersion than by SPM, dispersioncompensators are arranged with an almost equal interval and afterinfluences of SPM have been increased, they are arranged with smallerintervals. However positions, where the dispersion compensators arearranged in practice, can be changed in some extent, depending onpositions of optical relays and relay intervals.

Further, heretofore, a method is proposed, by which fiber in atransmission line has a slight normal dispersion and transmission iseffected while suppressing both worsening of the waveform in thetransmission line and nonlinear effects such as four light wave mixing,etc. by effecting dispersion compensation by using periodically abnormaldispersion fiber. The method for arranging dispersion compensatorsaccording to the present invention can be applied also to arrangement ofdispersion compensation fiber in such a dispersion compensatedtransmission.

FIG. 12 is a diagram showing the construction of a eighth embodiment ofthe present invention. In the present embodiment there are disposeddispersion compensators 106 and 107 at two positions, i.e. directlyafter the optical transmitter 100 and directly before the opticalreceiver 104, respectively. The dispersion compensator 106 has an effectto input signals to the transmission fiber after having given lightwaveform to be transmitted remarkable dispersion, deformedsatisfactorily the light waveform and reduced variations in intensity.For this reason it is possible to reduce significantly influences of SPMon the transmitted waveform. By this method the suppression of SPM canbe obtained e.g. by transmitting signals after having increased thewidth of the waveform to be transmitted to a value more than 1.5 timesas great as original one. It is possible to restore the transmittedwaveform by receiving it at the receiving end after having compensatedthe amount of dispersion of the dispersion compensator 106 or thedispersion compensator 106 and the transmission line by means of thedispersion compensator 107. It is possible also to divide thesedispersion compensators into several and to dispose them in thetransmission line, dispersed therein.

FIG. 13 is a diagram showing the construction of a ninth embodiment ofthe present invention. In the present embodiment it is supposed that thedispersion of optical fibers 110,111 and 112 constituting differentfiber sections fluctuates in a certain extent. In the prior artdispersion compensated transmission, fluctuations in the amount ofdispersion of the optical fiber are not taken into account at all. Incase where no dispersion compensation is effected, in such atransmission system, the transmission distance when all the amounts ofdispersion of optical fibers are minimum (on the negative dispersionside) is the smallest transmission distance. On the contrary, by thepresent method, dispersion compensation is effected so that an expectedvalue of the total amount of dispersion including dispersioncompensators disposed in the transmission line is a positive dispersion(abnormal dispersion). In this way, since the waveform after thetransmission is subjected to waveform distortion in the compressiondirection, it is possible to increase the smallest transmissiondistance. On the contrary, in case where mean dispersion of thetransmission line is occasionally on the positive dispersion side(abnormal dispersion), the transmission distance can be decreased by thedispersion compensation. However there is no problem, if this value isgreater than the smallest transmission distance of the transmissionline. Such an optimum value of the amount of dispersion compensation issuch a value that worsenings of the waveform after the transmission arein accordance with each other in two cases where all the amounts ofdispersion of different optical fibers are minimum and where all theamounts of dispersion of different optical fibers are maximum. At thistime the smallest transmission distance can be maximum.

FIG. 14 shows a tenth embodiment of the present invention, which is anexample, particularly in which only one dispersion compensator 106 isarranged before the optical receiver 104. FIG. 15 shows variations intransmittable distance, when the amount of dispersion of the dispersioncompensator 106 is varied. In the calculation, it is supposed that bitrate is 5 Gbps and fiber section length 1 =100 km and that the amount ofdispersion of optical fiber fluctuates in an extent of |D|≦3.5 ps/nm/kmand the limit of transmission is defined to be a point where thewaveform after the transmission is widened by about 25%. Two curves inthe figure show limits of transmission in cases where all the opticalfibers have an amount of dispersion of -3.5 ps/nm/km and where all theoptical fibers have an amount of dispersion of ±3.5 ps/nm/km,respectively, and in all the other cases the transmittable distance islonger than in either one of the cases. Consequently a region below thetwo curves represents distances, for which transmission can beguaranteed however strongly the amount of dispersion fluctuates. Fromthe figure it can be confirmed that the smallest transmission distanceis increased by effecting dispersion compensation on the abnormaldispersion side (on the right side in the figure), contrarily to thefact that the smallest transmission distance is about 700 km, in casewhere no dispersion compensation is effected. It is known that thesmallest transmission distance can be longest particularly by settingthe amount of dispersion at the intersection of the two curves (in theneighborhood of 2000 ps/nm in FIG. 15). This is just such an amount ofdispersion that worsenings of the waveform are approximately inaccordance with each other in the two cases where all the amounts ofdispersion of different optical fibers are minimum and where all theamounts of dispersion of different optical fibers are maximum.

Further, particularly when the transmittable distance in case where allthe amounts of dispersion of different optical fiber sections areminimum (negative dispersion or normal dispersion side) and the amountof dispersion compensation is zero is represented by L (700 km in FIG.15) and a positive dispersion compensation, with which transmission ispossible over the distance L in case where all the amounts of dispersionof different optical fiber sections are maximum is represented by C(about 3500 ps/nm in FIG. 1), it is possible to increase the smallesttransmission distance by setting the amounts of dispersion compensationof the optical dispersion compensators between 0 and C.

Further, in the case where a number of dispersion compensators arecontained, as indicated in FIG. 13, the amount of dispersioncompensation of each of the dispersion compensators can be determined asfollows. The amount of dispersion compensation C of the relevantdispersion compensator can be determined so that the worsening of thewaveform in case where all the amounts of dispersion of optical fibersections from the optical transmitters 100 to the relevant dispersioncompensator are minimum is approximately in accordance with theworsening in waveform in case where all the amounts of dispersion aremaximum. All the amounts of compensation C can be determined without anycontradiction by determining them one after another, as indicated above,starting from the dispersion compensator closest to the opticaltransmitter 100 in an order of increasing distance therefrom, and thesmallest transmission distance at this time is longest. The dispersioncompensators may be arranged either with an equal interval or withunequal intervals so that the interval decreases with decreasingdistance from the receiving end, as described previously.

A method called zero dispersion wavelength transmission is also studied,by which transmission is effected by choosing a zero dispersionwavelength, for which the amount of dispersion of the transmission lineis zero on the average in an optical fiber transmission. In such a zerodispersion wavelength transmission, heretofore it was not conceived toeffect dispersion compensation. This is because heretofore it wasthought that worsening of the transmitted waveform could be eliminatedby effecting transmission by using a zero dispersion wavelength. On thecontrary, in a reference

Technical Reports On Electronic Communication OCS93-24, by Kikuchi, etal., Electronic Communication Information Society (1993), it is shownthat significant worsening is produced in received waveform byinfluences of SPM, in case where the amount of dispersion of thetransmission line fluctuates. Since such worsening of the waveform isproduced by deviation of the amount of dispersion of the transmissionline, it is possible to cancel it by inserting dispersion compensators.For the amount of compensation of the dispersion compensators, althoughthe value satisfying Eq. (1) described previously is most suitable, aneffect can be obtained with an amount of compensation in a region from 0to a value about twice as great as the value given by Eq. (1).

In the zero dispersion wavelength transmission described above, even inthe case where the amount of dispersion of optical fiber fluctuates in acertain extent, it is possible to increase the smallest transmissiondistance by using dispersion compensation. In the zero dispersionwavelength transmission the two cases give rise to the worst dispersionarrangement, one of which is the case where the first half transmissionsection of the transmission line has the greatest amount of dispersion,while the second half transmission section has the smallest amount ofdispersion, as indicated in FIG. 16A, and the other of which is the casewhere the first half transmission section of the transmission line hasthe smallest amount of dispersion, while the second half transmissionsection has the greatest amount of dispersion, as indicated in FIG. 16B.In other cases the transmission distance is at least longer than eitherof those indicated in FIGS. 16A and 16B. Consequently it is possible toincrease the smallest transmission distance to the greatest by settingthe amount of compensation of the dispersion compensator 106 so thattransmission distances or worsenings in waveform after the transmissionin the two cases indicated in FIGS. 16A and 16B are equal to each other.It is possible to use a plurality of dispersion compensators also by thepresent method.

Since influences of SPM can be cancelled by setting amounts ofdispersion compensation of dispersion compensators so as to satisfy Eq.1, even if light output intensity is varied, received waveform is notvaried. Therefore effects can be obtained that it becomes easier to seta discrimination level in the optical receiver and that phase margin ofthe received waveform is increased. Further, since effects of SPM can beneglected, an effect can be obtained that design of a transmissionsystem becomes easier.

Further, since worsening of the waveform of the neighborhood of thereceiving end produced by SPM accumulated during transmission can becompensated with a high efficiency by the fact that arrangement intervalbetween dispersion compensators is smaller in the neighborhood of thereceiving end than in the neighborhood of the transmitting end, aneffect to increase transmission distance can be obtained. In addition aneffect to minimize the number of necessary dispersion compensators byarranging dispersion compensators at such positions that amounts ofworsening in waveform directly before different dispersion compensatorsare in accordance with each other.

Furthermore, since it is possible to reduce variations in intensity ofthe transmitted waveform by disposing dispersion compensators at twopositions directly after the optical transmitters and directly beforethe optical receiver and transmitting signals after having deformedsufficiently light waveform by the first dispersion compensator, aneffect to reduce influences of SPM can be obtained.

In case where the amount of dispersion of optical fibers constitutingdifferent fiber sections fluctuates in a certain extent, dispersioncompensation is effected so that an expected value of the total amountof dispersion including the dispersion compensators in the transmissionline is a positive dispersion (anomalous dispersion). Since the smallesttransmission distance of the transmission line is limited usually in thecase where all the amounts of dispersion of the transmission linefluctuate on the negative dispersion side, it is possible to increasethe smallest transmission distance of the transmission system bydispersion compensation on the positive dispersion side. Particularly,when amounts of dispersion compensation are so set that worsenings ofthe waveform are approximately in accordance with each other in twocases where all the amounts of dispersion of different optical fibersare minimum and where all the amounts of dispersion of different opticalfibers are maximum, an effect can be obtained that the smallesttransmission distance of the transmission system is maximum.

Also in the case where transmission is effected by using a zerodispersion wavelength of the transmission line, an effect to reduceworsening of the waveform by SPM and to increase the transmissiondistance by cancelling deviations of the amount of dispersion of thetransmission line by dispersion compensation. Further, even in the casewhere the amount of dispersion fluctuates in a certain extent, an effectto increase the smallest transmission distance of the transmissionsystem can be obtained by dispersion compensation on the positivedispersion side.

We claim:
 1. An optical transmission system having a total transmissiondistance L comprising an optical transmitter transmitting intensitymodulated optical signals; an optical fiber transmission line; anoptical receiver; and at least one optical dispersion compensator;wherein, denoting light intensity in an optical fiber at a point Z farfrom said optical transmitter by a distance z by P(z) and an amount ofdispersion from the point Z to said optical receiver (includingdispersion of said optical dispersion compensator) by D(z), a positionof said optical dispersion compensator and an amount of dispersion areso set that a value obtained by integrating a product P(z)·D(z) from z=0to L is approximately zero.
 2. An optical transmission system having atotal transmission distance L comprising:an optical transmittertransmitting intensity modulated optical signals; an optical fibertransmission line; an optical receiver; and at least one opticaldispersion compensator, wherein, denoting (1) light intensity in anoptical fiber at a point Z displaced from said optical transmitter by adistance z by P(z), (2) a point directly after an i-th opticaldispersion compensator by Z_(i) and (3) an amount of dispersion from thepoint Z to the point Z_(i) (including dispersion of optical dispersioncompensators) by D_(i) (z), where i is an index number for thedispersion compensators counting from the optical transmitter, positionsof said optical dispersion compensators and amounts of dispersion are soset that values obtained by integrating products P(z)·D_(i) (z) from z=0to Z_(i) are approximately zero for all i.
 3. An optical transmissionsystem comprising:an optical transmitter transmitting intensitymodulated optical signals; an optical fiber transmission line; opticalamplifiers used as repeaters dividing said optical fiber transmissionline into N (N>1) fiber sections; an optical receiver; and an opticaldispersion compensator disposed before said optical receiver, wherein anamount of dispersion C of said dispersion compensator is set so as to beapproximately {1/(aL)-(N+1)/(2N)} times as great as an amount ofdispersion B of said transmission line, where a is a loss factor of saidoptical fiber, and L is a total transmission distance.
 4. An opticaltransmission system comprising:an optical fiber transmission lineincluding at least one optical fiber transmission section; an opticaltransmitter, connected to a first end of the optical fiber transmissionline, transmitting intensity modulated optical signals, havingwavelengths approximately corresponding with a mean zero dispersionwavelength of the optical fiber transmission line; and an opticalreceiver, connected to a second end of the optical fiber transmissionline; and at least one optical dispersion compensator inserted betweenthe optical transmitter and the optical receiver, the at least oneoptical dispersion compensator having a dispersion characteristicopposite to that of the optical fiber transmission line.
 5. An opticaltransmission system having a total transmission distance L comprising atleast an optical fiber transmission line; and optical transmittertransmitting intensity modulated optical signals, whose wavelength isapproximately in accordance with a mean zero dispersion wavelength ofsaid optical fiber transmission line; an optical receiver; and at leastone optical dispersion compensator; wherein, denoting light intensity insaid optical fiber at a point Z far from said optical transmitter by adistance z by P(z) and an amount of dispersion from said point Z to saidoptical receiver (including dispersion of said light dispersioncompensator) by D(z), a position of said light dispersion compensatorand an amount of dispersion are so set that a value obtained byintegrating a product P(z)·D(z) from z=0 to L is approximately zero.